Question

If `a=hati+hatj+hatk, b=2hati+lambda hati+lambdahatj+hatk, c=hati-hatj+4hatk` and `a.(bxxc)=10` then `lambda` is equal to
A. 6
B. 7
C. 9
D. 10

Answer 1

Correct Answer - A
Given, `a=hati,hatj+hatk, b=2hati+lambdahatj+hatk and c=hati-hatj+4hatk`
Also, given `a.(bxxc)=10`
`Rightarrow [{:(,1,1,1),(,2,lambda,1),(,1,-1,4):}]=10`
`Rightarrow 1(4lambda+1-1(8-1)+1(-2-lambda)=10`
`Rightarrow 4lambda+1-7-2-lambda=10`
`Rightarrow 3lambda=18`
`Rightarrow lambda=6`